Answers
Answer:
obtuse
Step-by-step explanation:
A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...
f = a² +b² -c²
And the interpretation is ...
f > 0 . . . acutef = 0 . . . rightf < 0 . . . obtuse__
form factorFor the given side lengths, the form factor is ...
f = 11² +15² -20² = 121 +225 -400
f = -54
interpretationThe value is less than zero, signifying an obtuse triangle.
_____
Additional comment
The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.
This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.
Related Questions
Find the standard equation for the circle having the given center and radius.
center (0,0)
radius 7
Answers
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{0}{k})}\qquad \stackrel{radius}{\underset{7}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-0 ~~ )^2~~ = ~~7^2\implies x^2+y^2=49[/tex]
PLEASE HELP!! i’ll give brainliest and no bots!
Find the next two terms in this
sequence.
50, 40, 31, 23, 16, [?], [?]
Answers
Box and whisker plot measure of central tendency answers
Answers
One of the best things about box plots is that they include all of the measures of central tendency in one convenient package.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
The typical value of a set of data is known as the central tendency. We can measure central tendency in three different ways: mean, median, and mode.
Thus, one of the best things about box plots is that they include all of the measures of central tendency in one convenient package.
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wright the follwing in decimlal form:25/8
Answers
Answer:
25/8 in decimal form is 3.125.
Step-by-step explanation:
I hope this helps! :)
a five question multiple choice quiz has five choices for each answer. use the random number table provided, with 0's representing incorrect answers, and 1's representing correct answers to answer the following question: what is the experimental probability of correctly guessing at random exactly zero correct answers?
Answers
The experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, total multiple choice quiz = 5 questions
Each question contains 5 choices in which 1 choice is correct and remaining 4 are incorrect.
Possibility of first wrong choice = 4/5
Possibility of second wrong choice = 4/5
Possibility of third wrong choice = 4/5
Possibility of fourth wrong choice = 4/5
Possibility of fifth wrong choice = 4/5
Overall probability for Zero correct answer=(4X4X4X4X4)/(5X5X5X5X5)
= (4/5)⁵
Thus, the experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵
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The median of the values:29,24,30,23,28,18,
Answers
Answer:
26
Step-by-step explanation:
18,23,24,28,29,30
(6 in total + 1)/2=3.5.
- the number which is 3.5 is between 24 and 28.
- middle number between these two is 26.
Identify the national road that follows the coastline on the eastern side of the south Africa?
Answers
The name of the national road that follows the eastern coastline of South Africa is the N2.
Which road follows South Africa's eastern coastline?The N2 is a national road in South Africa that starts at Cape Town and goes towards the eastern part of South Africa.
It passes though Port Elizabeth, East London, Durban, and Richard's Bay which are all cities on the eastern side of South Africa and are along the coastline.
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Which of the following expressions is equivalent to (x5 y3 z2) (x4 y3 z6) for all real values of x y, and z ?
a. x9y6z8
b. x9y9z8
c. x20y6z8
d. x20y9z12
e. x21y6z12
Answers
The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression option is A x⁹y⁶z⁸. Hence, the correct option is A.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The expression is given as
(x⁵y³z²) and (x⁴y³z⁶)
Then, the product of the expression will be
= (x⁵y³z²) (x⁴y³z⁶)
= x⁵x⁴y³y³z²z⁶
= x⁵⁺⁴y³⁺³z²⁺⁶
= x⁹y⁶z⁸
Hence, the correct option is A x⁹y⁶z⁸.
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What is the greatest common factor of 30y^10 + 15y^6 + 5y^2?
30y^10
5y^2
y^2
5y^10
Answers
Answer:
5y²
Step-by-step explanation:
Prime factorizing each term :
⇒ 30y¹⁰ = 5 x 3 x 2 x y¹⁰
⇒ 15y⁶ = 5 x 3 x y⁶
⇒ 5y² = 5 x y²
===============================================================
From this, we understand the GCF of the numbers are :
⇒ 5 × y²
⇒ 5y²
Sheryl takes a summer job selling hats for a local soccer team. she realizes that there is a relationship between the number of games the team wins each season and the number of hats vendors like her tend to sell. she collects data from the past several seasons. the scatter plot shows her data and the line of best fit.
Answers
The equation of the line of fit and the data shows that the number of hats will be 48.
How to get the value?From the information, x games is won as y hats are sold. Therefore, the equation is given as:
y = 3.75x + 13.75
y = 3.75(9) + 13.75
y = 47.5
y = 48.
Therefore, the number of hats sold is 48.
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x+6/x+3 X x-6/x-3
A. 2x-12/x-3
B. x-12/x-6
C. x^2-12/x^2-6
D. x^2-36/x^2-9
Answers
d
Step-by-step explanation:
Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer
Answers
The age of Jennifer is 16.
What is Jennifer's age?Let Jennifer's age be represented with x
Jonathan's age would be 2x
The sum of their ages would be 48
2x + x = 48
3x = 48
x = 48 /3 = 16
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Answer: Jennifer is 16
Step-by-step explanation: 2x+y=48, divide by 3 then multiply by 2
help me please ill give expert for anyone who answers this
Answers
Answer:
see below
Step-by-step explanation:
There are two points where y = -3
at x = -2 and x = 1
when x = 0 f(0) = 1
Find the area of the smallest side of the right
triangle.
A = 169 ft²
A = 144 ft²
Answers
The area of the smallest side of the right triangle is 25 ft².
What is a right-angle triangle?A triangle having two sides at an angle of 90 degrees is called the right-angle triangle.
Note:- The figure is missing in the question I am attaching the complete figure with the answer below for calculation.
Given that:-
The hypotenuse = 169 ft ² = 13 ft
The side with area 144 ft² = 12 ft
Using Pythagoras' identity to find the third side x ( smallest )
x² + 12² = 13²
x² + 144 = 169 ( subtract 144 from both sides )
x² = 25 ( take the square root of both sides )
x = 5
Thus the area of the smallest side will be calculated as:-
A = 5²
A = 25 ft²
Therefore the area of the smallest side of the right triangle is 25 ft².
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10 points!! Help me out please!!
Answers
To solve this, we need to use our trigonometric equations
⇒ look at the diagram attached
Let's examine what the problem wants:
the length of the side adjacent to the 58-degree angleLet's examine what the problem gives us:
the length of the side opposite to the 58-degree anglethe angle that has a measure of 58-degreesLet's solve:
[tex]tan(58)=\frac{22}{x} \\22=x*tan(58)\\x=\frac{22}{tan(58)} \\x=13.75[/tex]
Answer: 13.8 (rounded to nearest tenth)
Hope that helps!
help only answer if you’re sure
Answers
Answer: D.
Step-by-step explanation:
5/9 + 2/4
find common denominator
common denominator=36
5 x 4=20 2 x 9=18
9 x 4=36 4 x 9=36
20/36 + 18/36
20 + 18=38
38/36 simplify
1 2/36 (if not in simpliest form)
5. Hunter deposited $750 into a certificate of deposit that earns 4.35% annual simple interest for 3
years. How much interest will Hunter earn?
Answers
Answer:
$97.875
Step-by-step explanation:
interest = 750 * 4.35% * 3
= $97.875
Is 9 a solution to the equation 21=3p-5? Show work
Answers
Answer:
No
Step-by-step explanation:
21 = 3p - 5
Step 1 : Add 5 on both sides
21 + 5 = 3p
26 = 3p
3p = 26
Step 2 : Divide 3 on both sides
p = 26/3
Hence, the solution of the given equation is 26/3, not 9.
Last month, a basketball team scored 83, 84, 85, 87, 89, 88, 67, 79, and 81 points in their games. Which data value(s) are outliers? Select all that apply.
Answers
The data value that is an outlier is 67
How to determine the outlier?The dataset is given as:
83, 84, 85, 87, 89, 88, 67, 79, and 81
To determine the outlier, we select the data values that are relatively far from others
In the above dataset, the data element 67 is far from other data values
Hence, the data value that is an outlier is 67
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Please help me thanks!
Answers
Part 1
V = pi*r^2*h .... volume of a cylinder
250 = pi*r^2*h
h = 250/(pi*r^2)
Plug this into the surface area of a cylinder equation
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )
SA = 2*pi*r^2 + 500/r
Now replace every copy of r with x to get this function
f(x) = 2*pi*x^2 + 500/x
x = radius
y = f(x) = surface area
Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.
Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).
The coordinates of that local min point will show up and they are (3.414, 219.689)
We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689
This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.
Use this value of r to find h
h = 250/(pi*r^2)
h = 250/(pi*3.414^2)
h = 6.828
Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.
Answer: This can has a radius of roughly 3.414 cm and height 6.828 cm.=============================================================
Part 2
Find the three side lengths of each triangle. So you should have 6 sides total. Then divide the corresponding sides to see if you get the same ratio. If so, then the triangles are similar by the side side side (SSS) similarity theorem. Another method is to find the angle between two sides and use the SAS (side angle side) similarity theorem. This is when the two pairs of sides form the same ratio, and the angles mentioned are congruent to each other. The angles must be between the sides used.A proportion can be used to solve equations based on similar polygons. For example, we could have the proportion x/2 = 30/10 which solves to x = 6.The first step is to multiply the two numbers. Then apply the square root to them. Example: The geometric mean of 4 and 9 is 6 because [tex]\sqrt{4*9} = \sqrt{36} = 6[/tex]Three numbers have the sum of 112. The first number is twice the second and the third number us twice the first. What is the smallest of the 3 numbers?
Answers
Answer:
x = 16
Step-by-step explanation:
Let the second number be x.
The first number = 2x
The third number = 2×2x = 4x
2x + x + 4x = 112
7x = 112
x = 112/7
x = 16
help help help me please
Answers
Answer:
1 and 3/4
Step-by-step explanation:
KCF, Keep Change Flip
7/6 divided by 2/3 becomes 7/6 multiplied by 3/2, which is 21/12
This can be simplified to 7/4, or 1 and 3/4
State fundamental theorems
Answers
Answer:
Step-by-step explanation:
Quincy's retirement party will cost $30 if he invites 10 guests. If there are 16 guests, how much will Quincy's retirement party cost? Solve using unit rates.
Answers
Answer:
it will cost $48
Step-by-step explanation:
30/10 = 3
3x6 = 18
18 + 30 = 48
Answer:
$48
Step-by-step explanation:
30/10 equals to 3/1 3 x 16 is 48
A company has a budget of $1,700 for a banquet. A banquet hall charges $150 to rent a room, plus $30 per guest. What is the maxiumum number of guests that can attend the banquet for the costs to remain under the budget?
Answers
Answer:
51 guests
Step-by-step explanation:
150+30x
1700=150+30x
1550=30x
x=1550/30=51
In a group of 32 musicians, all play piano, guitar, or both. Of those musicians, 12 only play guitar and 16 play both How many of the musicians play only piano
Answers
Answer:
4 only play piano
Step-by-step explanation:
12 + 16 = 28
32 - 28 = 4
what is the measure of
Answers
Answer:
what
Step-by-step explanation:
Which polynomial are in standard form
Answers
Answer:
A and C
Step-by-step explanation:
Exponent from biggest to lowest
Tips on how to study for GCSE’s
Answers
If f(t) = 2t3 find each value.
f(4)
3[f(t)]
Answers
The value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.
What is polynomia?To calculate the polynomial expression below, we use the technique below.
From the question,
Given:
f(t) = 2t³.............. Equation 1To find f(4) we substitute 4 as the value of x in equation 1
f(4) = 2(4³)f(4) = 512.To find 3[f(t)] we multiply equation 1 by 3
3[f(4)] = 3(2t³) = 6t³Hence, the value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.
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